(07-30-2014 12:19 PM)Owl 69/70/75 Wrote:  

(07-29-2014 10:33 AM)UM2001GRAD Wrote:  You are mistaken on this point. The question asked which would you expect. If you assume a normal distribution for each group and pluck one observation from each, you would expect the one from the distribution with a higher mean IQ to have the higher IQ. A better argument is that these IQ differences may be statistically significant, but they lack any practical significance in daily life because the differences aren't really that large.
There's a nice meta-analysis published last year (Zuckerman, Silberman, & Hall) that documents a negative relationship between measures of intelligence and religious beliefs. The more interesting part isn't that relationship, since that has been documented in various studies over many decades, but instead why that relationship exists. They offer several plausible explanations. It's an interesting read if you have access.

Umm, no.

You did touch, perhaps inadvertently, upon the key point. What you'd have to know in order to draw any inferences of the type addressed in the question, is not just the mean but also the distribution. Even with a normal distribution, you would need to consider not just the mean, but also the standard deviation, the extent to which the data points are scattered or not. A lower mean with a higher standard deviation might well produce a greater likelihood of BOTH 125 and 100 IQs than a higher mean with a lower standard deviation. Based on some data posted previously, I think in a prior response to this thread, the 125 would be slightly more than one standard deviation away from the mean for atheists, agnostics, and believers in most denominations, while 100 would be slightly less than one standard deviation away from the mean for most of those same groups. At that range, the level of correlation implied by the question would be fairly small, certainly not reasonable to say that you would EXPECT that result. The one thing that might be argued as saving the question is that the other choices are even more unlikely. That's why I originally said that my answer was "e. none of the above."

Also, you ASSUMED a normal distribution. That's not given in the problem. Nor is location given in the problem. I doubt you'd get the same result in Saudi, although it's probably reasonable to conclude that the question assumed Ohio. And in Ohio, whatever the difference in occurrence of both 125 and 100 IQs in both the Christian and atheist populations would probably be hugely outweighed by the Christian/atheist composition of the population as a whole. "Aine is a Christian and Theo is a Christian" is probably a far more likely outcome that "Aine is an atheist and Theo is a Christian."

In any event, the question is structured to suggest or imply that a 25 point gap in IQs in favor of atheists over Christians would be a reasonable expectation, and of course, nothing of the sort is even remotely true.

Of course I assumed a normal distribution. Anyone with even elementary econometric/statistical knowledge would be able to identify the distribution of IQs across large populations as being something that should follow a normal distribution pattern. If one of my students made this lame freshman-type argument you are making, I would ask them this simple question - why would you assume any other distribution, and would it matter if you did? The answers, of course, are that it makes no sense to assume some other distribution and that it wouldn't matter one iota if you did because you'd have to have some sort of reason to assume different distributions for the two populations being compared. And in academics, when not specified in a problem, ceteris paribus rules the day.

Then there is the half-cocked standard deviation thing (not sure if that's an argument or not) that you're talking about. Again, I would ask why you think the standard deviations between the populations in question would be significantly different. The answer is, of course, that they aren't significantly different according the data posted and the data I've seen in the half-dozen papers on the subject I've read in the past few days. So to assume they are significantly different is just plain wrong. Again, ceteris paribus would apply anyway since it wasn't specified.

So as I stated before, given the two assumed normal distributions with one observation from each, you expect the one plucked from the distribution with the higher mean to be the higher result and the one plucked from the lower mean to be lower result. It is statistically true.

The question at this point is whether you don't know enough about statistics to recognize the truth of what I'm saying or whether we're in another one of those "Owl never admits he's wrong even when he's clearly wrong" moments.

(07-30-2014 01:07 PM)UM2001GRAD Wrote:  The question at this point is whether you don't know enough about statistics to recognize the truth of what I'm saying or whether we're in another one of those "Owl never admits he's wrong even when he's clearly wrong" moments.

Any mirrors in your house?

(07-30-2014 01:09 PM)Smaug Wrote:  

(07-30-2014 01:07 PM)UM2001GRAD Wrote:  The question at this point is whether you don't know enough about statistics to recognize the truth of what I'm saying or whether we're in another one of those "Owl never admits he's wrong even when he's clearly wrong" moments.

Any mirrors in your house?

Plenty. And your accusation of hypocrisy in no way invalidates my very correct argument. Is there something useful you would like to add to the conversation?

(07-30-2014 01:13 PM)UM2001GRAD Wrote:  

(07-30-2014 01:09 PM)Smaug Wrote:  

(07-30-2014 01:07 PM)UM2001GRAD Wrote:  The question at this point is whether you don't know enough about statistics to recognize the truth of what I'm saying or whether we're in another one of those "Owl never admits he's wrong even when he's clearly wrong" moments.

Any mirrors in your house?

Plenty. And your accusation of hypocrisy in no way invalidates my very correct argument. Is there something useful you would like to add to the conversation?

Nah, I'm good, thanks.

(07-30-2014 01:14 PM)Smaug Wrote:  

(07-30-2014 01:13 PM)UM2001GRAD Wrote:  

(07-30-2014 01:09 PM)Smaug Wrote:  

(07-30-2014 01:07 PM)UM2001GRAD Wrote:  The question at this point is whether you don't know enough about statistics to recognize the truth of what I'm saying or whether we're in another one of those "Owl never admits he's wrong even when he's clearly wrong" moments.

Any mirrors in your house?

Plenty. And your accusation of hypocrisy in no way invalidates my very correct argument. Is there something useful you would like to add to the conversation?

Nah, I'm good, thanks.

No problem. Drop back in anytime.

(07-30-2014 01:07 PM)UM2001GRAD Wrote:  So as I stated before, given the two assumed normal distributions with one observation from each, you expect the one plucked from the distribution with the higher mean to be the higher result and the one plucked from the lower mean to be lower result. It is statistically true.

Yes, but when the difference between the two means is 2-5 points, and the difference in the observed values is 25 points, and each of the observed values is about one standard deviation away from either mean, one would reasonably infer that the difference is most likely attributable to some other attribute or combination of attributes.

(07-30-2014 01:58 PM)Owl 69/70/75 Wrote:  

(07-30-2014 01:07 PM)UM2001GRAD Wrote:  So as I stated before, given the two assumed normal distributions with one observation from each, you expect the one plucked from the distribution with the higher mean to be the higher result and the one plucked from the lower mean to be lower result. It is statistically true.

Yes, but when the difference between the two means is 2-5 points, and the difference in the observed values is 25 points, and each of the observed values is about one standard deviation away from either mean, one would reasonably infer that the difference is most likely attributable to some other attribute or combination of attributes.

The difference based on the one study's data above is 5 points between athiests and christians. The observed value on the right is almost exactly one standard deviation for the athiest population and almost exactly 1.5 standard deviations for the christian group. That .5 standard deviation is a big deal. On the left, the observed value is only .5 standard deviations from the mean for the christian group and nearly a full standard deviation for the athiest group. Again, that .5 standard deviation is a big deal. The actual data in that chart backs up the inference in the exam question, which is secondary to the fact that the ceteris paribus nature of an academic question means that the 5 point difference in means is enough for the inference to be appropriate.

I was nice enough to give you a reasonable line of opposition to the issue, but you persist in pushing an obviously wrong statistical argument. Just stop. You're not helping yourself at all.

No, I'm not pursuing a wrong argument. But I will stop because this isn't going anywhere.

(07-28-2014 10:00 PM)HeartOfDixie Wrote:  

(07-28-2014 09:51 PM)smn1256 Wrote:  If you're gonna insult an entire group of people then do it right.

Be careful with the 'O' word.

normally I would not get involved in this sort of post,

the citations for "Race, Evolution, and Behavior" are a total joke.

(07-30-2014 03:50 PM)Owl 69/70/75 Wrote:  No, I'm not pursuing a wrong argument. But I will stop because this isn't going anywhere.

Sure.

(07-28-2014 09:43 PM)UCGrad1992 Wrote:  

(07-28-2014 09:20 PM)chargeradio Wrote:  http://dailycaller.com/2014/07/26/ohio-s...hristians/

#1 - As we've seen time and time again, these days it's open season on Christianity and this is an example of a more subtle or passive aggressive attack on the faith.
#2 - It's not just happening at Ohio State but on college campuses all across the country conservative and christian values are increasingly facing intolerance at institutions that are supposed to stand for equality, tolerance and freedom of thought, ideas and opinion.
#3 - If this was actually true I'll take the lower IQ and live on comfortably in my beliefs and values any day of the week and twice on Sundays.

ISIS is after Christians too.